Age Estimation of Transmission Line Using Statistical Health Index and Failure Probability Curve-Fitting Method

Abstract

The aging process of transmission lines has a direct impact on the reliability and safety of the power grid. Therefore, an accurate age estimation method is imperative for effective maintenance planning and infrastructure investment. This paper introduces a systematic methodology for estimating the age of overhead transmission lines, utilizing the percentage statistical health index (%SHI) and the failure probability curve-fitting (FPCF) method. The %SHI, employing a scoring and weighting approach derived from test results and inspections, is used to assess the actual condition of transmission line equipment. Additionally, the FPCF approach is applied to illustrate the connection between the SHI and the likelihood of failure, facilitating the assessment of transmission line age by fitting failure probability curves to the SHI data. This age is directly associated with the probability of experiencing a failure. The evaluation was conducted on 924 towers situated along four transmission lines connecting the 115 kV substations S1–S2, S3–S4, S5–S6, and S7–S8. These transmission lines are in four regions with diverse terrain and environments such as mountains, rice fields, and more. In the SHI calculation, practical testing results and historical failure data were applied. The results clearly indicate that there were notable disparities in the age estimations for transmission lines in diverse geographical regions of Thailand when compared to their actual ages. These discrepancies can be attributed to various factors, including the local environment, such as rainfall, flooding, and salt-laden air as well as specific geographical features like mountainous and coastal terrain. To mitigate the deterioration of transmission lines in all regions, it is essential to implement a proactive maintenance strategy. This strategy should involve more frequent inspections, the use of advanced monitoring technologies, and the establishment of robust maintenance procedures, with which it would become possible to enhance the accuracy of equipment condition assessments, ultimately resulting in an overall improvement in the reliability of transmission lines.

1. Introduction

Electricity has become a fundamental element in the daily lives of people, impacting various sectors, including industry and commerce. It plays a crucial role in a country’s development. The efficiency and reliability of the electric power transmission system in a country are paramount, along with operational flexibility requirements, which indicate the capability of a power grid to cope with diverse operating conditions and fluctuating demands while upholding reliability. To ensure system reliability, continuous maintenance is essential to mitigate potential risks and minimize costs. Consequently, the effective utilization of tools and technology is imperative for risk management and the enhancement of power transmission system reliability.

In a power transmission system, its components can be categorized into eight groups: conductors, conductor accessories, insulators, steel structures, foundations, lightning protection, tower accessories, and the right of way [1,2], as illustrated in Figure 1.

These components degrade over time due to various factors, including percentage load, system utilization, voltage levels, contingency analysis, historical failure records, age, societal considerations, pollution, and human impact [3,4]. The current state of overhead transmission lines is a pivotal factor in determining the timing of maintenance or replacement. This decision not only ensures the continued functioning of the transmission system but also serves to minimize the costs associated with replacing older overhead transmission lines with new ones. As a result, it is of utmost importance to establish a precise and practical method for evaluating the age and remaining life of overhead transmission lines. This assessment plays a central role in the decision-making process regarding maintenance or replacement. The actual condition of overhead transmission lines is a critical factor in determining when maintenance or replacement should be scheduled to maintain the transmission system and in reducing the investment costs of a new overhead transmission lines replacing aging ones. Therefore, it is essential to have a precise and reasonable method for assessing the age and remaining life of overhead transmission lines as a key factor in the decision-making process for maintenance or replacement.

In this research, an age assessment method for transmission lines was implemented, relying on statistical data derived from the percentage health index (%HI) calculation [5,6,7] of overhead transmission lines. This statistical %HI was established using a scoring and weighting method [8]. The outcomes of these %HI assessments were then utilized to construct a statistical curve, depicting the relationship between the %HI and the probability of failure. This statistical analysis employed a normal distribution, also known as a Gaussian distribution or bell curve [9,10]. Normal distributions are widely used in statistical analysis in reliability engineering and statistical analyses where understanding the lifespan or durability of components is crucial. In practice, lifetime estimation by using a normal distribution is often employed. The assumption is that the lifetimes of these entities conform to a normal distribution, making it easier to make statistical predictions and calculations regarding the expected duration or failure rates. It elucidates the connection and pattern between the %HI and the probability of failure. This valuable insight is subsequently used to gauge the remaining life of the overhead transmission lines.

Estimating the age of overhead transmission lines uses information about expected deterioration to plot the relationship between age and the probability of failure. This was accomplished using the Gompertz–Makeham mortality model [11,12,13], which describes the dynamics of equipment degradation in high-voltage transmission systems [14]. The aging was then evaluated by comparing the probability of failure values from the %HI curve with the life–probability curve of the high-voltage grid.

2. Health Index of Transmission Line

As shown in Figure 2, the %HI serves as a valuable tool for ranking the maintenance requirement of high-voltage transmission equipment according to their its conditions. It is determined through the analysis of test results and inspections, which include visual examinations, electrical testing, and chemical analysis [15,16]. The calculation of the %HI necessitates the collection and scrutiny of test data, facilitating the identification of components that may need repair or replacement to preserve the condition of the transmission line.

In references [17,18,19], the analytic hierarchy process (AHP) was innovatively employed as a multi-attribute decision-making support tool tailored for the identification of critical components in power transmission systems. The application specifically addresses concerns related to system reliability and optimal performance. These references delve into various models, methods, concepts, and applications of the AHP, with a notable emphasis on its role in the multiple criteria assessment of substation conditions through pair-wise comparisons.

Subsequently, a %HI is determined utilizing the weighting and scoring method (WSM). The AHP method is employed to calculate the weights, while the scores are assigned based on various test methods and their respective results. The assessment rating system is organized into six levels, ranging from 0 to 5, where each rating corresponds to a specific condition: 0 (very bad condition), 1 (poor condition), 2 (fair condition), 3 (satisfactory condition), 4 (good condition), and 5 (very good condition) [20]. This method provides a systematic way to evaluate and categorize the health and condition of the components in assessing substation health and functionality.

2.1. Condition Assessment Criteria of Transmission System

Several testing approaches to assess the condition of all eight groups in Figure 2 are derived from diverse standards and references. These include the Australian criteria for inspecting overhead transmission line equipment [21,22], the Cigre Brochure, and the Cigre Session [23,24], as well as articles on the maintenance of overhead transmission lines available in IEEE Xplore [25]. Together, these sources formed a comprehensive compilation of testing methods, as detailed in

Table 1. Testing methods of equipment in overhead transmission lines.

Group	Sub-Components	Testing Method
Conductor	Conductor	Visual inspection, loss of zinc, tensile strength, torsional ductility
Conductor Accessory	Damper	Visual inspection
	Spacer	Visual inspection, special test
	Dead end	Resistance, thermography
	Joint	Resistance
	PG clamp	Thermography
Insulator	Insulator	Visual inspection, visual inspection of fitting, thermography
Steel Structure	Tower	Monopole visual inspection, concrete pole visual inspection, steel lattice visual inspection
	Anchor and guy	Visual inspection, tensile strength
Foundation	Foundation	Grillage visual inspection, concrete visual inspection, NDT test of concrete, stub visual inspection
Lightning Protection	OHGW/OPGW	Visual inspection, loss of zinc, tensile strength, visual inspection of fitting
	Marker ball	Visual inspection
	Grounding system	Earth resistance, visual inspection
Tower Accessory	Danger sign	Visual inspection
	Phase plate	Visual inspection
Right of Way	Right of way	Visual inspection, OW distance

, for the test methods used in an electric power utility system in Thailand. A detail explanation about the methods applied to assess the technical condition of overhead transmission line used by an electric power utility system in Thailand and how to transform the physical condition into a scoring number have been thoroughly explained in [26].

2.2. Determination Weights Using Analytic Hierarchy Process

The importance weights for the eight major component groups and their associated testing methods were established using the analytic hierarchy process (AHP). The AHP is a methodology utilized to compute the weights of all testing methods, facilitating decision-making and the prioritization of alternatives when addressing a particular issue [17,18,19]. This approach enables experts from diverse organizations to collaborate, pooling their expertise to collectively establish the criteria for assessing the condition of overhead transmission line equipment.

2.3. Health Index Determination Using Scoring and Weighting Methods

The %HI for assessing the condition of overhead transmission lines is determined by using the weighting and scoring method, as represent by Equation (1) [6].

$$\%HI=\frac{\sum _{i=1}^M(S_i\times W_i)}{\sum _{i=1}^M(S_{max,i}\times W_i)}\times 100\%$$

(1)

where S_i is the score reflecting the actual condition of each transmission line, S_max,i is the maximum score achievable for each transmission line, W_i is the weight assigned to each transmission line, and M is the total number of transmission lines considered.

3. Age Estimation through Relative %HI to Probability of Failure Model

The determination of age involves utilizing a relative model that links the statistical %HI with the probability of failure [27,28]. This process comprises five steps, starting with the plotting of a normal distribution curve to depict the correlation between the %HI and the probability density, as shown in Figure 3a. Subsequently, the survival function is employed to generate a relative curve representing the relationship between the %HI and the probability of failure, as illustrated in Figure 3b. The third step involves applying the failure function to plot a curve depicting the connection between age and the failure rate, as displayed in Figure 3c. Next, the cumulative probability of failure function is applied to establish a curve representing the relationship between age and the probability of failure, as showcased in Figure 3d. Lastly, the health curve (left) and life curve (right) are fitted with the same probability of failure to estimate the age of the transmission line, facilitating the appropriate maintenance based on both age and %HI.

3.1. Health Index Curve Using Normal Distribution

A normal distribution is firstly applied in constructing the %HI curve. The majority of the data exhibit a central or average tendency. There are relatively few data points that deviate significantly from this mean value. To work with a normal distribution, it is essential to identify the mean and standard deviation of the data. Specifically, for the %HI values and transmission line failure probability values, the mean and standard deviation were determined using the standard normal distribution denoted as per [29] in Equation (2).

$$z=\frac{x-\mu }{\sigma }$$

(2)

where z corresponds to the standard normal distribution table, x represents the %HI, µ is the mean, and σ is the standard deviation of the provided data.

Once the mean and standard deviation have been determined, these values are utilized to calculate the probability density based on the %HI value, as indicated in Equation (3) [9,10]. The outcome of this calculation is presented in Figure 3a, which displays a curve depicting the relationship between the %HI and the probability density.

$$f\left(x\right)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}$$

(3)

where f(x) represents the probability density, x is the %HI, µ is the mean, and σ is the standard deviation.

The probability density is computed based on these parameters. Subsequently, when these calculated values are plotted, a normal distribution curve is obtained. The probability of failure is determined by finding the area under the cumulative curve of the probability density curve, as specified in Equation (4) [9,10]. The resulting relationship between the %HI and the probability of failure is illustrated in Figure 3b, which presents a curve depicting this relationship.

$$R\left(x\right)={\int }_x^{\infty }f\left(x\right)dx$$

(4)

where $R\left(x\right)$ is the probability of failure and $f\left(x\right)$ is the probability density.

In the curve depicted in Figure 3b, illustrating the relationship between the %HI and the probability of failure, one can observe the trend of the failure probability within the %HI range from 0 to 100. This curve represents the degradation pattern of the transmission line.

3.2. Life Curve Using Gompertz–Makeham Mortality Model Based Failure Function

The scarcity of failure rate data of transmission lines is primarily due to ongoing maintenance practices. However, it is important to note that the most common pattern for transmission line failures is an exponential increase in frequency with age. This implies a growing risk of future damage as the transmission lines age. Then, the Gompertz–Makeham mortality model [9,14] can be applied. This model aligns with the exponential acceptance of equipment aging and mortality pattern and can be described by Equation (5).

$$f\left(t\right)=\gamma e^{\beta \left(t-\alpha \right)}$$

(5)

where $f\left(t\right)$ is the failure rate, $t$ is age of the transmission line (years), and β and α are constant parameters controlling the shape of the failure curve.

Figure 3c illustrates the relationship between age and the failure rate with an age vs. failure rate curve. This curve provides insight into how the failure rate of transmission lines tends to increase exponentially as they age, indicating the risk of damage as the lines get older.

Determining the likelihood of device failure involves employing the Gompertz–Makeham mortality model failure rate equation. The computation of the device’s probability of failure can be accomplished by utilizing the mortality model, as outlined in Equation (6). Figure 3d illustrates a curve depicting the relationship between age and the probability of failure. This methodology is anticipated to yield a more precise and closer estimation of the device’s probability of failure.

$$P_f\left(t\right)=1-e^{-\frac{e^{\beta \left(t-\alpha \right)}- e^{-\alpha \beta }}{\beta }}$$

(6)

where $Pf\left(t\right)$ is the probability of failure, $t$ is age of the transmission line (years), and β and α are constant parameters controlling the shape of the curve.

In Figure 3d, a curve of age vs. the probability of failure is presented. This curve visually represents how the probability of failure changes with the age of the device. It offers a useful illustration of how the probability of failure tends to increase with the device’s age based on the mortality model.

3.3. Single Population Mean Using Student’s t-Distribution

Confidence intervals (CI) for age estimates were examined to assess the reliability of age estimates. This can be done using Student’s t-distribution [30] as a statistical method for drawing conclusions about the population mean in situations with a limited sample size and an uncertain population standard deviation. The essential steps in this estimation process include initiating data collection with a random and representative sample, computing the sample mean and standard deviation, setting a significance level (α), establishing degrees of freedom, and acquiring the critical value for analysis. Subsequently, the margin of error is determined by multiplying the critical value by the standard error of the mean. The standard error is the sample standard deviation divided by the square root of the sample size, as written in Equation (7).

$$EBM=(t_{\frac{\alpha }{2}})(\frac{S}{\sqrt{n}})$$

(7)

where EBM is the margin of error for the population mean, t(α/2) represents the t-score such that the area to the right is equal to α/2, S is the standard deviation, and n is the sample size or the amount of data.

The next step involves determining the CI by computing a range for the population mean, which can be achieved by both adding and subtracting the margin of error from the sample mean and is typically expressed as per Equation (8).

$$CI=\overline{x}\pm EBM$$

(8)

where $\overline{x}$ is the sample mean, and $EBM$ is the error bound for the population mean.

Lastly, the interpretation of the CI becomes crucial as it offers a range of values where the population mean is expected to reside with the selected level of confidence. This approach enables the estimation of the population mean while quantifying the associated uncertainty. The choice of the t-distribution over the normal distribution is motivated by the need to address added uncertainty stemming from small sample sizes and unknown population standard deviations.

4. Results and Discussion

The age of the transmission lines is estimated in this section. Firstly, the %HI curve is analyzed by using a normal distribution and is shown in Section 4.1. Next, the life curve is analyzed by using the Gompertz–Makeham mortality model. The probability of failure, which is compared with age using a mortality model, is shown in Section 4.2. Then, the transmission line age is estimated from the health indices using the probability of failure and the difference between the estimated and actual age was obtained, as shown in Section 4.3.

4.1. Health Index Curve Analysis Using Normal Distribution

To analyze the probability density and the probability of failure of a %HI by using a normal distribution, the two required parameters are the mean and standard deviation. Utilizing the data presented in

Table 2. Determined %HI and probability of failure.

Zone	%HI	Risk	Probability of Failure	z	μ	σ
Paddy field	45	Very high	80%	0.85	57.57	14.79
	54	High	60%	0.26
	62	Medium	40%	−1.75
	70	Low	20%	−0.84
Mountain plain	52	Very high	80%	0.85	63.57	13.61
	60	High	60%	0.26
	67	Medium	40%	−1.75
	75	Low	20%	−0.84
Water way	41	Very high	80%	0.85	53.57	14.79
	50	High	60%	0.26
	58	Medium	40%	−1.75
	66	Low	20%	−0.84

, the %HI values were substituted into Equation (1). This analysis yielded the following results: for paddy fields, the mean and standard deviation were 57.57 and 14.79; for mountain plains, they were 63.57 and 13.61; and for waterways, they were 53.57 and 14.79. Subsequently, these mean and standard deviation values were employed to compute the probability density and probability of failure of the %HI using Equations (2) and (3), as illustrated in

Table 3. Probability density and probability of failure of %HI.

%HI	Paddy Field		Mountain Plain		Water Way
	f(x)	R(x)	f(x)	R(x)	f(x)	R(x)
0	0.000012	0.999987	0.000001	0.999999	0.000032	0.999964
5	0.000041	0.999836	0.000003	0.999989	0.000103	0.999577
10	0.000128	0.999352	0.000013	0.999944	0.000295	0.998441
15	0.000360	0.997961	0.000048	0.999768	0.000760	0.995449
20	0.000906	0.994378	0.000163	0.999161	0.001748	0.988393
25	0.002038	0.986110	0.000481	0.997321	0.003599	0.973482
30	0.004104	0.969020	0.001252	0.992401	0.006632	0.945258
35	0.007395	0.937375	0.002869	0.980801	0.010934	0.897402
40	0.011924	0.884886	0.005786	0.956697	0.016131	0.824710
45	0.017205	0.806892	0.010271	0.912542	0.021297	0.725796
50	0.022215	0.703072	0.016051	0.841244	0.025159	0.605223
55	0.025667	0.579273	0.022080	0.739755	0.026596	0.473557
60	0.026537	0.447027	0.026735	0.612407	0.025159	0.344756
65	0.024551	0.320473	0.028496	0.471542	0.021297	0.231884
70	0.020326	0.211983	0.026735	0.334186	0.016131	0.143274
75	0.015058	0.128667	0.022080	0.216117	0.010934	0.080958
80	0.009982	0.071349	0.016051	0.126652	0.006632	0.041699
85	0.005921	0.036025	0.010271	0.066892	0.003599	0.019542
90	0.003143	0.016523	0.005786	0.031703	0.001748	0.008341
95	0.001493	0.006878	0.002869	0.013439	0.000760	0.003268
100	0.000635	0.002605	0.001252	0.005082	0.000295	0.001210

.

From the details provided in Table 3, two %HI curves were produced to illustrate the relationships between the probability density and the percentage of the HI curve, which is presented in Figure 4a, and the probability of failure and the %HI curve, which is presented in Figure 4b. This analysis took into account the distinctive characteristics of the paddy field zone, the mountain plain zone, and the waterway zone of the transmission system. In Figure 4a, it is clear that the mountain plain zone experienced the highest concentration of failures, despite having a higher percentage of the %HI compared to the other zones. Conversely, the waterway zone demonstrated a better preservation of the %HI with a lower probability density. Moreover, Figure 4b illustrates that the probability of failure (R(x)) was highest in the mountain plain zone, even with its higher %HI. In conclusion, this implies that the transmission lines in the mountain plain zone were more likely to experience failure compared to the other zones.

4.2. Life Curve Analysis Using Gompertz–Makeham Mortality Model

The analysis of the failure rate and probability of failure for the transmission line life was analyzed by applying the Gompertz–Makeham mortality model. This model characterizes the failure rate and probability of failure, both of which depend on two parameters, i.e., α and β. To calculate these parameters, the data from

Table 4. Age values and probability of failure established.

Zone	Age (Years)	Risk	Probability of Failure	β	α
Paddy field	75	Very high	80%	0.065	110
	67	High	60%
	58	Medium	40%
	46	Low	20%
Mountain plain	71	Very high	80%	0.069	103
	63	High	60%
	55	Medium	40%
	44	Low	20%
Water way	81	Very high	80%	0.060	120
	72	High	60%
	62	Medium	40%
	49	Low	20%

, including the age and probability of failure values, were utilized. By substituting these values into Equation (5), the values for α and β were determined. For the paddy field zone, the calculated values were α = 110 and β = 0.065. In the mountain plain zone, α was 103 and β was 0.069, and for the water way zone, α was 120 and β was 0.060. Subsequently, these determined values of α and β were applied to calculate the failure rate (f(t)) and probability of failure (P_f(t)) for various ages using Equations (5) and (6), respectively. The comprehensive results of these calculations are presented in

Table 5. Failure rate and probability of failure of age.

Age (Years)	Paddy Field		Mountain Plain		Water Way
	f(t)	Pf(t)	f(t)	Pf(t)	f(t)	Pf(t)
0	0.000785	0.000000	0.000819	0.000000	0.000747	0.000000
5	0.001086	0.004626	0.001157	0.004880	0.001008	0.004344
10	0.001503	0.010994	0.001634	0.011731	0.001360	0.010178
15	0.002081	0.019740	0.002307	0.021323	0.001836	0.017998
20	0.002880	0.031717	0.003257	0.034709	0.002479	0.028457
25	0.003986	0.048053	0.004599	0.053299	0.003346	0.042398
30	0.005517	0.070209	0.006493	0.078940	0.004517	0.060900
35	0.007635	0.100025	0.009168	0.113966	0.006097	0.085309
40	0.010567	0.139720	0.012946	0.161166	0.008230	0.117255
45	0.014625	0.191788	0.018279	0.223562	0.011109	0.158616
50	0.020242	0.258692	0.025810	0.303844	0.014996	0.211390
55	0.028015	0.342251	0.036443	0.403268	0.020242	0.277416
60	0.038774	0.442588	0.051457	0.519960	0.027324	0.357862
65	0.053665	0.556712	0.072657	0.646945	0.036883	0.452436
70	0.074274	0.677159	0.102592	0.771212	0.049787	0.558396
75	0.102797	0.791833	0.144858	0.876006	0.067206	0.669665
80	0.142274	0.886591	0.204538	0.947788	0.090718	0.776763
85	0.196912	0.951069	0.288806	0.984605	0.122456	0.868467
90	0.272532	0.984713	0.407791	0.997255	0.165299	0.935593
95	0.377192	0.996945	0.575797	0.999760	0.223130	0.975434
100	0.522046	0.999671	0.813020	0.999992	0.301194	0.993312

. Following the data shown in Table 5, Figure 5a,b display the two life curves: the failure rate concerning age, which is shown in Figure 5a, and the probability of failure relative to age, which is shown in Figure 5b. These figures encompass the data from the paddy field zone, mountain plain zone, and waterway zone. They visually demonstrate the progressive rise in the likelihood of a transmission line experiencing failure across the entire age from 0 to 100 years.

From Figure 5, it can be seen that the failure rates and probabilities of failure for the transmission lines were diverse in the different geographical zones with distinct characteristics. In the mountain plain zone, it was identified that there exists the highest failure rate and probability of failure. This area is characterized by a blend of mountainous landscapes and flat expanses, presenting difficulties in the upkeep of transmission lines. The paddy field zone had the second-highest failure rate and probability of failure because the constant presence of water in the flooded rice paddies may lead to soil erosion, corrosion of the transmission infrastructure, and an increased susceptibility to electrical faults. Meanwhile, the waterway zone exhibited the lowest failure rate and probability of failure. This can be attributed to the environmental benefits of water bodies, which dissipate heat, reduce stress on the transmission infrastructure, and provide a protective barrier against certain external factors.

4.3. Age Analysis Using Relative Health Index to Probability of Failure Model

The estimation of the age of the transmission lines was conducted based on historical %HI data that are linked to the failure probability. The %HI plays a crucial role in determining the probability of failure by referencing the failure probability curve and comparing it with the %HI. The results for the three sample transmission lines are depicted in Figure 6, Figure 7 and Figure 8. To provide specific details, in the paddy field zone, a %HI of 78.20% corresponded to a failure probability of 0.100197. In the mountain plain zone, a %HI of 89.64% was associated with a failure probability of 0.039145. Meanwhile, in the waterway zone, a %HI of 74.73% corresponded to a failure probability of 0.094210. Utilizing these failure probabilities to estimate the age of the transmission lines, we derived approximate ages of 35.03 years for Figure 6, 21.35 years for Figure 7, and 36.53 years for Figure 8.

A similar comprehensive evaluation was conducted on 924 towers situated across four transmission lines connecting the 115 kV substations S1–S2, S3–S4, S–S6, and S7–S8. As a result of this assessment, a scattering of data of the estimated ages was obtained for these towers, as depicted in Figure 9, while

Table 6. Age estimation and age difference with actual age of 40 transmission towers.

HVTL Tower’s Name	Zone	%HI	Actual Age	Estimated Age	Age Difference	HVTL Tower’s Name	Zone	%HI	Actual Age	Estimated Age	Age Difference
115 kV S1–S2#10	Mountain plain	71.80	40	50.52	+10.52	115 kV S5–S6#20	Mountain plain	69.17	35	54.04	+19.04
115 kV S1–S2#20	Mountain plain	77.64	40	41.92	+1.92	115 kV S5–S6#40	Mountain plain	68.10	35	55.40	+20.40
115 kV S1–S2#30	Paddy field	74.42	40	41.31	+1.31	115 kV S5–S6#60	Water way	76.77	35	32.73	−2.27
115 kV S1–S2#40	Paddy field	71.88	40	45.30	+5.30	115 kV S5–S6#80	Mountain plain	68.42	35	55.00	+2.00
115 kV S1–S2#50	Mountain plain	70.45	40	52.35	+12.35	115 kV S5–S6#100	Water way	76.16	35	33.89	−1.11
115 kV S1–S2#60	Mountain plain	74.20	40	47.12	+7.12	115 kV S5–S6#120	Mountain plain	70.74	35	51.98	+16.98
115 kV S1–S2#70	Paddy field	78.94	40	33.76	−6.24	115 kV S5–S6#140	Mountain plain	82.21	35	34.42	−0.58
115 kV S1–S2#80	Paddy field	74.82	40	40.64	+0.64	115 kV S5–S6#160	Mountain plain	73.53	35	48.10	+13.10
115 kV S1–S2#90	Paddy field	76.78	40	37.42	−2.58	115 kV S5–S6#180	Mountain plain	78.03	35	41.32	+6.32
115 kV S1–S2#100	Paddy field	77.04	40	37.00	−3.00	115 kV S5–S6#200	Mountain plain	82.64	35	33.70	−1.30
115 kV S3–S4#38	Mountain plain	71.16	48	51.40	+3.40	115 kV S7–S8#18	Paddy field	76.32	22	38.20	+16.20
115 kV S3–S4#76	Water way	74.50	48	36.96	−11.04	115 kV S7–S8#36	Paddy field	96.59	22	6.35	−15.65
115 kV S3–S4#114	Mountain plain	62.99	48	61.49	+13.49	115 kV S7–S8#41	Water way	87.30	22	13.72	−8.28
115 kV S3–S4#152	Water way	75.31	48	35.47	−12.53	115 kV S7–S8#72	Paddy field	70.52	22	47.34	+25.34
115 kV S3–S4#190	Mountain plain	77.26	48	42.53	−5.47	115 kV S7–S8#90	Paddy field	81.40	22	29.49	+7.49
115 kV S3–S4#228	Mountain plain	75.61	48	45.05	−2.95	115 kV S7–S8#104	Mountain plain	96.59	22	10.18	−11.82
115 kV S3–S4#266	Water way	74.16	48	37.58	−10.42	115 kV S7–S8#126	Paddy field	88.17	22	17.77	−4.23
115 kV S3–S4#304	Mountain plain	65.41	48	58.69	+10.69	115 kV S7–S8#143	Water way	90.71	22	8.90	−13.10
115 kV S3–S4#342	Mountain plain	75.61	48	45.05	−2.95	115 kV S7–S8#162	Paddy field	88.17	22	17.77	−4.23
115 kV S3–S4#380	Mountain plain	79.60	48	38.79	−9.21	115 kV S7–S8#180	Mountain plain	88.17	22	23.95	+1.95

shows the age estimation and age difference with the actual age of 40 transmission towers from these four transmission lines, presenting insight into specific cases.

It is evident from the information provided in Figure 9 and Table 6 that the age estimation results for the transmission lines in the different geographical regions of Thailand showed variations in the estimated age compared to the actual age. Let us summarize the observations:

(1)

The 115 kV S1–S2 transmission line (northeastern Thailand): This transmission line is located in a region with limestone mountains, forests, and fertile plains, as presented in Figure 10a. The results indicate that the estimated age was higher than the actual age, resulting in a high age difference, particularly in the mountainous area.

(2)

The 115 kV S3–S4 transmission line (southern Thailand): This transmission line is located in the southern part of Thailand, where the landscape includes a mix of coastal areas and limestone mountains, as depicted in Figure 10b. In the southern part of Thailand, where the landscape includes a mix of coastal areas and limestone mountains, the results also show a higher estimated age than the actual age, particularly in the mountainous area.

(3)

The 115 kV S5–S6 transmission line (southern Thailand): This transmission line is situated in a region with lower-lying landscapes, including plains and coastal areas, as illustrated in Figure 10c. The region experiences significant rainfall during the wet season, which can lead to flooding in low-lying areas and along water bodies.

(4)

The 115 kV S7–S8 transmission line (northeastern Thailand): In this area, the transmission line runs through paddy fields, which are characterized by standing water or flooded conditions, as shown in Figure 10d. The results show a higher estimated age than the actual age, particularly in the paddy fields. This was likely due to the challenging environmental conditions in flooded fields, which can affect the condition of transmission components.

These observations highlight the influence of the local environment and terrain on the age estimation results of transmission lines. It is important to consider these factors when assessing the condition and maintenance needs of power transmission infrastructure in different geographical regions. Accurate age estimation is crucial for ensuring the reliability and safety of transmission lines. The results can be concluded as follows.

Lines S1–S2, S3–S4, and S5–S6 are located in particularly in mountainous areas, and the results showed a higher estimated age than the actual age. Several factors contribute to the deterioration of transmission lines, as follows. Firstly, mountainous areas often pose challenges for infrastructure maintenance. The rugged terrain can make it difficult for maintenance crews to access the transmission lines, leading to a reduced maintenance frequency and effectiveness. This limited access can result in slower responses to equipment wear and tear. In addition, coastal areas and limestone mountains can subject the transmission lines to diverse environmental conditions. Coastal areas may expose equipment to saltwater and humidity, leading to corrosion and faster aging. Meanwhile, limestone mountains may have extreme temperature fluctuations, which can impact the condition of the equipment. Thirdly, mountainous areas are prone to natural disasters such as landslides, rockfalls, and tree falls. These natural disasters result in physical harm to transmission line components, expediting their deterioration. Lastly, the weather conditions in mountainous areas are also characterized by fluctuations in temperature and humidity, which can affect the rate of equipment deterioration and cause the service life of transmission lines to be overestimated. Therefore, reducing transmission line deterioration in these terrains requires a proactive maintenance approach. Inspections are implemented, such as visual inspection, advanced testing techniques, etc., which results in effective maintenance practices. Modifying transmission line age estimates to respond to terrain and environmental conditions results in estimates that can increase equipment efficiency and transmission line reliability.

The 115 kV S7–S8 transmission line in northeastern Thailand, which runs through paddy fields with flooded conditions, showed a higher estimated age than the actual age, particularly in the paddy fields, which can be attributed to several factors related to the challenging environmental conditions in the flooded fields. Here are some possible explanations: The condition of the transmission line can be attributed to several factors related to the challenging environmental conditions in flooded fields. Firstly, corrosion and erosion in paddy fields due to their standing water can accelerate the corrosion and erosion of transmission line components. Exposure to water and soil with varying chemical compositions can lead to the deterioration of equipment over time. Next, limited maintenance access in flooded fields can present a challenge to access for maintenance and inspections. The standing water makes it difficult for maintenance crews to reach the equipment, reducing the frequency and effectiveness of maintenance activities. Thirdly, the continuous submersion of transmission components in water can affect their performance and longevity. It can lead to moisture ingress, which may affect the electrical and mechanical integrity of the equipment. Lastly, monitoring the condition of equipment in submerged conditions can be more complex, and detecting issues may be delayed, leading to overestimations of age. For example, transmission tower number 72 of line 115 kV S7–S8 had an estimated age of 47.34 years, which was much greater than the actual age. This was because it is a transmission pole traversing a rice field submerged in water in a flooding area during the rainy season. This extreme environmental condition leads to the severe aging of such towers. Upon examination of its condition, it was observed that the conductors displayed a textured surface, gaps between threads, and protruding rusty wires. The damper indicated some corrosion, featuring a rough and rusty surface. Examination of the insulation and coating disclosed the presence of dirt, galvanization, and pin corrosion. The steel structure showed a surface color with a noticeable roughness and signs of zinc corrosion. The foundation also displayed evidence of corrosion. Moreover, in its right-of-way, there were trees and clusters of bamboo that could pose potential hazards. These abnormal conditions caused a drastic reduction in the condition assessment scores and a poor %HI, leading to a greater estimated age than the actual age.

4.4. Percentage Confidence Interval

The next step involved calculating the percentage confidence interval (%CI) for the estimated age of the transmission lines across all the locations to provide precise and comprehensive results. The %CI is a statistical measure that offers a range or interval of values in which the estimated age of transmission lines is expected to be found with a particular level of confidence, typically expressed as a percentage. It serves as a useful tool for quantifying the uncertainty associated with age estimations.

In this case, a 95% confidence interval was set to analyze the estimated age of the transmission lines. This means that 95% of the estimated age values could be considered confident as a precise estimated age because they fell within the specified interval, while there was approximately a 5% error in the estimated ages of the transmission lines. The remaining 5% represents a margin of error, which allows for the possibility that the estimated age may fall outside the interval due to uncertainty or variability in the estimation process, resulting in an approximately 5% chance of error in the estimated ages of the transmission lines. The %CI and its related parameters of the transmission lines in the different zones are presented in

Table 7. Values of %CI and its related parameters of transmission lines in different zones.

Details	HVTL’s Name
	115 kV S1–S2		115 kV S3–S4		115 kV S5–S6		115 kV S7–S8
	Paddy Field	Mountain Plain	Mountain Plain	Water Way	Mountain Plain	Water Way	Paddy Field	Mountain Plain	Water Way
n	88	47	360	20	141	77	153	13	17
s	5.40	5.20	8.85	13.77	10.14	11.63	14.11	9.09	9.78
t(α/2)	1.987	2.015	1.984	2.093	1.984	1.992	1.984	2.160	2.110
EBM	1.14	1.53	0.93	6.45	1.69	2.64	2.26	5.45	5.00
$\overline{\mathrm{x}}$	37.78	45.72	51.92	41.68	46.84	37.20	18.07	20.67	10.29
95% confidence interval	36.63–38.92	44.19–47.25	50.99–52.85	35.23–48.12	45.14–48.53	34.56–39.84	15.80–20.33	15.23–26.12	5.29–15.30

, while the average age estimation was also calculated for the different zones, as shown in

Table 8. Average age estimation of the lines falling within %CI in different zones.

Details	HVTL’s Name
	115 kV S1–S2		115 kV S3–S4		115 kV S5–S6		115 kV S7–S8
	Paddy Field	Mountain Plain	Mountain Plain	Water Way	Mountain Plain	Water Way	Paddy Field	Mountain Plain	Water Way
No. of towers (towers)	88	47	360	20	141	77	153	13	17
Actual age (years)	40	40	48	48	35	35	22	22	22
Average age (years)	37.78	45.72	51.92	41.68	46.84	37.20	18.07	20.67	10.29
Standard deviation	5.40	5.20	8.85	13.77	10.14	11.63	14.11	9.09	9.78
Median	36.93	45.99	52.87	41.60	47.03	37.34	15.13	19.53	8.90
Mode	33.76	41.92	45.05	-	50.48	24.78	3.59	19.48	1.86
95% confidence interval	36.63–38.92	44.19–47.25	50.99–52.85	35.23–48.12	45.14–48.53	34.56–39.84	15.80–20.33	15.23–26.12	5.29–15.30

.

Based on the data provided in Table 7, it was determined that the 115 kV transmission lines S1–S2 in the paddy field zone possessed an average tower age of 37.78, falling within the 95% confidence interval that ranged from 36.63 to 38.92. Similarly, in the mountain plain zone, the average tower age for transmission lines S1–S2 was 45.72, also within the 95% confidence interval between 44.19 and 47.25.

Regarding the 115 kV transmission lines S3–S4 in the mountain plain zone, the average pole age was 51.92, lying within the 95% confidence interval that ranged from 50.99 to 52.85. In the waterway zone, the average pole age was 41.68, also within the 95% confidence interval that spanned from 35.23 to 48.12.

Concerning the 115 kV transmission lines S5–S6 in the mountain plain zone, the average pole age was 46.84, which was within the 95% confidence interval that ranged from 45.14 to 48.53. In the waterway zone, the average pole age was 37.20, falling within the 95% confidence interval that ranged from 34.56 to 39.84.

Conclusively, for the 115 kV transmission lines S7–S8 in the paddy field zone, the average pole age was 18.07, which was within the 95% confidence interval between 15.80 and 20.33. In the mountain plain zone, the average pole age was 20.67, which was within the 95% confidence interval that spanned from 15.23 to 26.12. In the waterway zone, the average pole age was 10.29, which was also within the 95% confidence interval that ranged from 5.29 to 15.30.

5. Conclusions

In conclusion, this research focused on the age estimation of overhead transmission lines, employing a comprehensive approach that combined the percentage statistical health index (%SHI) and the failure probability curve-fitting (FPCF) method. The aging of transmission lines has a direct impact on the reliability and safety of the power grid. Accurate age estimation is of paramount importance for effective maintenance planning and infrastructure investment.

This paper presented a systematic methodology that utilized the SHI with a scoring and weight method, derived from test results and inspections, to assess the actual condition of transmission line equipment. Furthermore, the FPCF approach was employed to model the relationship between the SHI and the likelihood of failure, allowing for the estimation of transmission line age by fitting the failure probability curves to the SHI data. This age estimation is closely associated with the probability of experiencing a failure.

The evaluation encompassed 924 towers situated along four transmission lines that connect the 115 kV substations S1–S2, S3–S4, S5–S6, and S7–S8, spanning across four regions with diverse landscapes and environments, including mountains and paddy fields, among others. In the %SHI calculation, practical testing results and historical failure data were integrated.

The results of this study clearly indicate notable disparities in the age estimations for the transmission lines in diverse geographical regions of Thailand when compared to their actual ages. These discrepancies can be attributed to various factors, including the local environment, such as rainfall, flooding, and salt-laden air, as well as specific geographical features like mountainous and coastal terrain.

To counteract the deterioration of transmission lines in all regions, it is imperative to implement a proactive maintenance strategy. This strategy should involve more frequent inspections, the use of advanced monitoring technologies, and the establishment of robust maintenance procedures. By addressing the unique challenges posed by the terrain and environmental conditions, it becomes possible to enhance the accuracy of equipment condition assessments, ultimately resulting in an overall improvement in the reliability of transmission lines.